Question

1 point
2.A car moves along a straight
line, whose equation of motion
is given by x=12t+3t^2, where x in
metre, t in second, the velocity
of the car at the start will be
​

Answer 1

Explanation:

x = 12t + 3t²

We know that v = dx/dt

Differentiating with respect to dt on both sides

dx/dt = d(12t + 3t²)/dt

We know that d(a + b)/dt = da/dt + db/dt

Therefore,

v = d(12t)/dt + d(3t²)/dt

We know that,

d(x^n)/dt = nx^(n-1)

v = 12 + 6t

Here we want the velocity of the car at the start, i.e t = 0

Therefore,

v = 12 + 6(0) = 12 m/s